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Lesson 1

1. Lesson 1

1.2. Are You Ready?

Mathematics 20-2 M3 Lesson 1

Module 3: Quadratics

 
Are You Ready?
  1.  
    1. Complete the following data table for the relation y = 2x + 4.

      x

      0

      1

      2

      3

      −1

      −2

      0.5

      y

      		              

      Answer

    2. Draw a graph from the table of values from part a. Join the data points in a smooth curve. If you do not have graph paper of your own, you can use 1-cm Grid Paper. Answer
  1.  
    1. Complete the following data table for the quadratic relation y = x2 + 2.

      x

      0

      1

      2

      3

      −1

      −2

      0.5

      y

      		              

      Answer

    2. Draw a graph from the table of values. Join the data points in a smooth curve. Answer

    1. Complete the following data table for the quadratic relation y = −5(x − 1)2 + 5.

      x

      0

      1

      2

      0.5

      1.5

      y

      		          

      Answer

    2. Draw a graph from the table of values. Join the data points in a smooth curve. Answer
  1. This chart shows how much water vapour (in grams) a kilogram of air can hold at different temperatures.

    Temperature

    (°C)

    Water Vapour

    (g/kg of air)

    −40

    0.1

    −35

    0.2

    −30

    0.3

    −25

    0.51

    −20

    0.75

    −10

    1.8

    0

    3.8

    5

    5

    10

    7.8

    15

    10

    20

    15

    25

    20

    30

    27.7

    35

    35

    40

    49.8


    1. What is the domain of the relation? Answer

    2. What is the range of the relation? Answer

    3. Make a graph of the relation. Answer 
  1. For each set of graphs, state which graph is a function and which graph is not a function. Explain how you know.


    1. This shows a graph with a parabola opening to the left. This shows a graph with a parabola opening upwards.

      Answer


    2. This graphic shows a grid with dots at (0, 0), (2, 4), (4, 8), (6, 4), (8, 16), (10, 10), (12, 15), (14, 14), (16, 7), (18, 3), and (20, 18.5). This graphic shows a grid with dots at (0, 0), (2, 4), (4, 6), (6, 9), (8, 6), (10, 8), (14, 9), (14, 12), (14, 14), (16, 8), and (18, 3).

      Answer


    3. This shows a graph with a circle. This shows a graph with a straight line moving upwards the farther it moves along the x- and y-axes.

      Answer

  2. For each of the following figures, tell which figures are functions and which are not. Give a reason for your answer.

    Figure A shows two ellipses with the left ellipse containing the numbers 1 to 4 and an arrow from each number to a number in a second ellipse with the numbers -2, 15, 6, and 10: 1 points to -2, 2 points to 15, 3 points to 6, 4 points to 10. Figure B shows two ellipses with the left ellipse containing the numbers 1 to 4, and the right ellipse containing the numbers -2 and 6: 1 and 2 point to -2 while 3 and 4 point to 6.

     

    Figure C shows two ellipses with the left ellipse containing the numbers 1 to 4, and the right ellipse containing the numbers -2, 6, 10, and 15: 1 points to -2, 2 points to both -2 and 15, 3 points to 6, and 4 points to both 6 and 10. Figure D shows two ellipses with the left ellipse containing the numbers 1 and 2, and the right ellipse containing the numbers -2, 6, 10, and 15: 1 points to -2, 15, and 6 while 2 points to 15, 6, and 10.

     

    Answer

     

  3. For each of the following ordered pairs, tell which sets are functions and which are not. Give a reason for your answer.






    Answer

If you successfully completed the Are You Ready? questions, move on to the Discover section of the lesson.

 

If you experienced difficulties with the questions, use the resources in the Refresher section to review the concepts before continuing through the lesson.